Bifurcation and forced symmetry breaking in Hamiltonian systems

Fethi Grabsi (1) , James Montaldi (2) , Juan-Pablo Ortega (3)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 UMIST - Department of Mathematics
3 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We consider the phenomenon of forced symmetry breaking in a symmetric Hamiltonian system on a symplectic manifold. In particular we study the persistence of an initial relative equilibrium subjected to this forced symmetry breaking. We see that, under certain nondegeneracy conditions, an estimate can be made on the number of bifurcating relative equilibria.

Keywords: Differential geometry, dynamical systems

Domains: Exactly Solvable and Integrable Systems [nlin.SI]

Fethi Grabsi, James Montaldi, Juan-Pablo Ortega. Bifurcation and forced symmetry breaking in Hamiltonian systems. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 338 (7), pp.565-570. ⟨10.1016/j.crma.2004.01.029⟩. ⟨hal-00015288⟩